LC resonant clock resource minimization using compensation capacitance

ABSTRACT

VLSI distributed LC resonant clock networks having reduced inductor dimensions as well as simplified decoupling capacitances that are obtained by including one or more compensation capacitors. A compensation capacitor can be added in parallel with a clock capacitance and/or in parallel with a clock inductor. The presence of a compensation capacitance reduces the overhead associated with the inductor and the decoupling capacitor. The compensation capacitor (s) can be selectively switched into the network to create scalable resonant frequencies.

FIELD OF THE INVENTION

The presently disclosed subject matter is directed towards clockdistribution networks that use distributed inductor-capacitor (LC)resonant tanks. More particularly, the present invention relates to theuse of compensation capacitors to reduce the overhead of on-chip tankresources of Very Large Scale Integration (VLSI) clock distributionnetworks while enabling frequency scaling of resonant clocks.

BACKGROUND OF THE INVENTION

The on-going demand for high performance electronic systems has driventhe need for high-speed Very Large Scale Integration (VLSI) chips. VLSIimplementations are demand driven to proceed in two inter-relateddirections: higher performance and higher density (more devices per unitarea). While modern VLSI chips have achieved astonishingly high levelsof performance and chip density the demand for even higher levels keepsgrowing.

A serious impediment to achieving higher performance and higher densityis power consumption. As a general rule higher performance requires morepower, which produces more heat, which increases failure rates which canrender VLSI devices unsuitable for some tasks. The result is that powerconsumption is often the predominant challenge in improving highperformance VLSI devices.

Almost all modern VLSI devices are clocked. As long as all gates cankeep up the higher the clock rate the faster the performance. As clockrates and VLSI devices densities increase it becomes difficult to ensurethat all gates can be properly clocked. One reason for this is that eachsequential gate element in a VLSI device needs its own clock signal, butnot all sequential gate elements are the same distance from the clocksource. This means that all clock lines are not the same length and thusassociated parameters such as distributed capacitances and resistancesdiffer between elements. Different lengths coupled with unavoidablesignal delays caused by distributed resistances and capacitances cancause clock signals to arrive at different elements at different times.This is referred to as clock skew.

Compounding VLSI clocking problems is that clocking requires power. Infact, the on-chip clock distribution network (CDN) of modern VLSIdevices often consume more than 35% of the total device power and canoccasionally require as much as 70%. This is expected since dynamicpower is determined by:P=αCV²f

where α is the switching activity, C is the clock distribution network(CDN) capacitance, V is the supply voltage and f is the operatingfrequency.

Many works have attempted to reduce power consumption by decreasing oneor more of these factors, but the savings are often limited during peakactivity and the requirement that clock quality must not be degraded.

One successful approach to reducing VLSI power consumption is the use ofDistributed LC resonant clocks. Referring now to FIG. 1, a distributedLC resonant clock network 2 circumvents problems by oscillating inputenergy 4 between electrical potentials and magnetic fields using aparallel clock capacitance C_(clk) 6 and an inductance L 8. Anadditional decoupling capacitance C_(d) 10 offsets the voltage range to0-V_(dd) by forming a series LC tank with the inductance L 8.

The approach shown in FIG. 1 has proven the power savings of distributedLC resonant clocks. Distributed LC resonant clocks have also been shownto have stable clock phases and magnitudes when compared to alternativeapproaches such as standing waves and rotary/salphasic resonant clocks.Academic algorithms have further optimized distributed LC resonantclocks to show the possibility of power savings of up to 90%.Unfortunately, such large power savings come at the expense ofrelatively large inductors and decoupling capacitors.

Inductors such as the inductor 8 of FIG. 1 can be readily fabricatedon-chip. For example, VLSI spiral inductors can be manufactured on-chipusing well-known CMOS processes. For example, high-Q spiral inductorscan be fabricated using modern processes with thick (˜10 μm) oxides.But, on-chip VLSI inductors come with parasitic resistances andcapacitances that decrease the inductor quality factor. But parasiticresistances can be included in the model of the inductor, and parasiticcapacitances can be treated as part of the decoupling capacitance in aresonant clock. FIG. 2 shows a square spiral inductor L 14 having aninductance that can be approximated as:

$L = {0.0002\mspace{11mu}{l\; 〚{{\ln\frac{2l}{w + t}} + 0.5 + \frac{w + t}{3l}}〛}\mspace{11mu}{nH}}$

where n is the number of turns, w is the width of a trace, t is thethickness of the metal, l is the length of trace and s is the spacingbetween turns. Given n, s, w, d_(i) (inner diameter of the square spiralinductor), d_(o) (outer diameter of the square spiral inductor) the chipareas occupied by the inductor L 14 is:Area=d ₀ ²=(d _(i)+2n(s+w))²

On-chip capacitors are most effectively created as MOS(metal-oxide-semiconductor) capacitors that have both parallel-plate andfringe-field capacitances as illustrated by capacitor 20 shown in FIG.3. The capacitance of capacitor 20 can be approximated as:

$C = {{C_{pp} + C_{fringe}} = {{\frac{e_{di}}{t_{di}}{WL}} + \frac{2\pi\; e_{di}}{\log( \frac{t_{di}}{H} )}}}$

where W and L are the width and length of the metal representing thearea of the capacitor, H is the height of the metal, and ε_(di) andt_(di) are the permittivity and thickness of the dielectric layer. Inthe case of SiO₂, ε_(di)=ε_(r) ε₀=3.9×8.854×10⁻¹² F/m, where ε_(r) isthe relative permittivity of the insulating material, and ε_(o) is thepermittivity of free space.

As the W/H ratio reduces below unity the fringing capacitance of thecapacitor 20 becomes dominate and significantly contributes to theoverall capacitance. In a modern 90 nm CMOS technology, a MOS capacitor20 can reach a capacitive density of 10˜20 fF/μm².

These on-chip VLSI inductors and capacitors can be used to form a seriesor parallel LC “tank” circuit which resonates at a particular frequency.The resonant frequency f_(r) of an ideal LC tank is the frequency whenthe network has zero total reactance. The resonant frequency of a tank(C and L) is ideally:

${fr} = \frac{1}{2\pi\sqrt{LC}}$

When the impedance of the LC tank is near infinite due to the reactancescancelling the drive capability requirement of the clock buffer isminimized and clock energy can be saved.

Referring once again to FIG. 1, the resonant clock topology contains twoLC tanks: one parallel and one series. The parallel LC tank ideally hasinfinite impedance at resonance while the series impedance ideally haszero impedance. These tanks would counteract each other if they resonateat the same frequency. Therefore, the decoupling capacitor C_(d) 10 istypically much larger than C_(clk) 6 to separate the resonantfrequencies of the parallel LC_(clk) and extra series LC_(d) tanksaccording to½π√{square root over (LC _(d))}<<½π√{square root over (LC _(clk))}

This ensures a wide margin such as f_(clk)/f_(d)˜3 by making C_(d) 10for example 10 times C_(clk) 6 or more. The magnitude at the resonantfrequency, w₀=2πf₀ is referred to as the characteristic impedance of thedistributed LC resonant clock network 2.

In practice, the inductor L 8 area is the most significant obstacle towidespread acceptance of distributed LC resonant clock networks. Anotherproblem is that the decoupling capacitance C_(d) 10 represents an extraburden on that acceptance. Reducing the inductor area and simplifyingthe decoupling capacitance would be highly beneficial and would makedistributed LC resonant clock networks more practical.

Another issue with the wide spread acceptance of distributed LC resonantclock networks is achieving a configurable frequency of operationwithout significant efficiency degradation. Frequency scaling would behighly advantageous.

Therefore a distributed LC resonant clock network having reducedinductor dimensions would be beneficial. Even more beneficial would be adistributed LC resonant clock network having a simplified decouplingcapacitance. Ideally such a distributed LC resonant clock networkideally would enable scalable frequency resonant clocks.

BRIEF SUMMARY OF THE INVENTION

The present invention discloses an LC resonant clock network having acompensation capacitor C_(c) in parallel with a capacitor C_(clk) and/orin parallel with an inductor. Those compensation capacitors can bepermanently placed in parallel or switched into place.

The principles of the present invention provide for distributed LCresonant clock networks having reduced inductor dimensions as well assimplified decoupling capacitances. Furthermore, the principles of thepresent invention provide for scalable frequency distributed LC resonantclock networks.

A distributed LC resonant clock network in accord with the presentinvention minimizes inductor and capacitor overhead using and addedcoupling capacitor. That added coupling capacitor also enables scalablefrequency.

A VLSI clock distribution network in accord with the present inventionincludes a VLSI substrate, a clock distribution capacitor C_(clk)fabricated on the VLSI substrate and having a lead that is connected toground and an open lead. A decoupling capacitor C_(d) is also fabricatedon the VLSI substrate as is a clock distribution inductor L. Theinductor L connects to the open lead and to the decoupling capacitor. Abuffer is also fabricated on the VLSI substrate with the buffer drivingthe capacitor C_(clk) and the inductor L at a clock frequency. Acompensation capacitor C_(c) is in parallel with the capacitor C_(clk).The clock distribution network is resonant at a clock frequency set by:

$f_{clk}^{\prime} = {\frac{1}{2\pi}{\sqrt{\frac{C_{clk} + C_{c} + C_{d}}{{L( {C_{clk} + C_{d}} )}C_{d}}}.}}$

The capacitor C_(clk), the capacitor C_(d), and/or the capacitor C_(c)are fabricated as MOS capacitors. The inductor L is beneficially aspiral wound inductor having an inductance approximately equal to:

$L = {0.0002\mspace{11mu}{l\; 〚{{\ln\frac{2l}{w + t}} + 0.5 + \frac{w + t}{3l}}〛}\mspace{11mu}{{nH}.}}$

Another VLSI clock distribution network that is in accord with thepresent invention includes a VLSI substrate, a clock distributioncapacitor C_(clk) fabricated on the VLSI substrate and having a leadthat is connected to ground and an open lead. A decoupling capacitorC_(d) is also fabricated on the VLSI substrate as is a clockdistribution inductor L. The inductor L connects to the open lead and tothe decoupling capacitor. A buffer is also fabricated on the VLSIsubstrate with the buffer driving the capacitor C_(clk) and the inductorL. A compensation capacitor Cc is in parallel with the inductor L. Theclock distribution network is resonant at the clock frequency which isdetermined as:

$f_{clk}^{\prime} = {\frac{1}{2\pi}{\sqrt{\frac{C_{clk} + C_{d}}{L\lceil {{C_{clk}C_{d}} + {C_{c}( {C_{clk} + C_{d}} \rceil}} }}.}}$

The capacitor C_(clk), the capacitor C_(d), and/or the capacitor C_(c)are fabricated as MOS capacitors. The inductor L is beneficially aspiral wound inductor having an inductance approximately equal to:

$L = {0.0002\mspace{11mu}{l\; 〚{{\ln\frac{2l}{w + t}} + 0.5 + \frac{w + t}{3l}}〛}\mspace{11mu}{{nH}.}}$

Another VLSI clock distribution network that is in accord with thepresent invention includes a VLSI substrate, a clock distributioncapacitor C_(clk) fabricated on the VLSI substrate and having a leadconnected to ground and an open lead. A decoupling capacitor C_(d) isfabricated on the along with a clock distribution inductor L. Theinductor L is connected to the open lead and to the decouplingcapacitor. A buffer is also fabricated on the VLSI substrate. The bufferdrives the capacitor C_(clk) and the inductor L at a clock frequency.The VLSI clock distribution network further includes a firstcompensation capacitor C_(c1) that is connected to ground and a firstpass switch that is disposed between the first compensation capacitorC_(c1) and the lead. The selectable resonant frequency changes when thefirst pass switch closes.

The frequency scalable VLSI clock distribution network may also includea second pass switch and a second compensation capacitor that are inseries. The series combination of the second pass switch and thecapacitor C_(c2) are in parallel with the inductor L. The selectableresonant frequency changes when the second pass switch closes.

BRIEF DESCRIPTION OF THE DRAWINGS

The advantages and features of the present invention will become betterunderstood with reference to the following detailed description andclaims when taken in conjunction with the accompanying drawings, inwhich like elements are identified with like symbols, and in which:

FIG. 1 illustrates a prior art distributed LC resonant clock network 2;

FIG. 2 illustrates a spiral inductor 14 suitable for use in the presentinvention;

FIG. 3 illustrates a MOS capacitor 20 suitable for use in the presentinvention;

FIG. 4 is a schematic depiction of a distributed LC resonant clocknetwork 50 that is in accord with the present invention;

FIG. 5 illustrates the Miller Effect in distributed LC resonant clocknetwork 50;

FIG. 6 illustrates a distributed LC resonant clock network 100 thatprovides for selectable frequency scaling; and

FIG. 7 illustrates a VLSI device 200 including a VLSI chip that carriesLC resonant clocks in accord with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The presently disclosed subject matter now will be described more fullyhereinafter with reference to the accompanying drawings in which oneembodiment is shown. However, it should be understood that thisinvention may take different forms and thus the invention should not beconstrued as limited to the specific embodiment set forth herein.

All publications mentioned herein, specifically including “DISTRIBUTEDRESONANT CLOCK GRID SYNTHESIS,” a patent application 61/502,626 filed onJun. 22, 2011 having inventors Dr. Matthew Guthaus and Xuchu Hu, areincorporated by reference for all purposes to the extent allowable bylaw.

In addition, in the figures like numbers refer to like elementsthroughout. Additionally, the terms “a” and “an” as used herein do notdenote a limitation of quantity, but rather denote the presence of atleast one of the referenced items.

FIG. 7 illustrates a VLSI device 200 including a VLSI chip 204. The VLSIdevice 200 further includes a protective package 202 that spaces theVLSI chip 204 above internal contacts (shown as ball contacts) as wellas external ball contacts 208. The VLSI chip 204 is suitable forcarrying the LC resonant tanks that form the VLSI clocks.

FIG. 4 illustrates a distributed LC resonant clock network 50 that is inaccord with the present invention and which illustrates two differenttopologies for insertion of a compensation capacitance C_(c) 54. Oneposition is in parallel with C_(clk) 56 while the other in parallel withL 58. In addition, FIG. 4 includes a signal source 60 operating at f₀,an amplifier 62, and a decoupling capacitor C_(d) 66.

If C_(c) 54 is in parallel with C_(clk) 56 the size of the inductance L58 can be reduced to obtain the same frequency f₀ according to theformula:

$f_{0} = \frac{1}{2\pi\sqrt{LC}}$

However, if C_(c) 54 is in parallel with L 58 the often undesired MillerEffect can be used to good effect. Its application is shown in FIG. 5which suggests that C_(c) 54 can be divided as C_(c1) and C_(c2) inparallel with, and thus adding to C_(clk) 56 and C_(d) 66, respectively.This reduces the size of both L 58 and C_(d) 66 to obtain the sameoperating frequency f₀. In this manner the impact of a relatively smallcapacitor can be magnified to great advantage in distributed LC resonantclock network while still retaining the required very high frequencyoperation.

If both the parallel and series tank circuits are considered in thedistributed LC resonant clock network 2 of FIG. 1 the resonant clockfrequency becomes:

$f_{clk} = {\frac{1}{2\pi}\sqrt{\frac{C_{clk} + C_{d}}{{LC}_{clk}C_{d}}}}$

If as usual C_(d)=10C_(clk) this reduces to:

$f_{clk} = {\sqrt{\frac{11}{10}} \times \frac{1}{2\pi\sqrt{{LC}_{clk}}}}$

The result is a 4.9% increase in resonant frequency due to the parasiticseries LC_(d) tank. That fact alone can be utilized to reduce therequired inductor size of L 58 and save area at a fixed frequency f₀.

Referring again to FIG. 4, if C_(c) 54 is added in parallel with C_(clk)56 the resonant frequency will add C_(c) 54 to C_(clk) 54 to give aresonant frequency of:

$f_{clk}^{\prime} = {\frac{1}{2\pi}\sqrt{\frac{C_{clk} + C_{c} + C_{d}}{{L( {C_{clk} + C_{d}} )}C_{d}}}}$

The result is a decrease in resonant frequency given by:

$\frac{f_{clk}^{\prime}}{f_{clk}} = \sqrt{\frac{1 + \frac{C_{c}}{C_{clk} + C_{d}}}{1 + \frac{C_{c}}{C_{clk}}}}$

Now if C_(c) 54 is added in parallel with L 58 the resonant frequencyis:

$f_{clk}^{\prime} = {\frac{1}{2\pi}\sqrt{\frac{C_{clk} + C_{d}}{L\lceil {{C_{clk}C_{d}} + {C_{c}( {C_{clk} + C_{d}} )}} \rceil}}}$

The result is a decrease in resonant frequency found by.

$\frac{f_{clk}^{\prime}}{f_{clk}} = \sqrt{\frac{1}{1 + \frac{C_{c}}{C_{clk}} + \frac{C_{c}}{C_{d}}}}$

This result is even better as far as reducing the size of the inductorthan putting C_(c) in parallel with C_(clk) 56.

A specific example may be helpful. If C_(c)=0.5×C_(clk) andC_(d)=10×C_(clk), then the resulting clock f′_(clk) given C_(c) 54 is inparallel with C_(clk) 56 in FIG. 4 is:

$f_{clk} = {{\sqrt{\frac{11}{15}} \div 2}\pi\sqrt{{LC}_{clk}}}$

Now, if Cc 54 is in parallel with L 58 then:

$f_{clk} = {{\sqrt{\frac{11}{15.5}} \div 2}\pi\sqrt{{LC}_{clk}}}$

This suggests that in the tank network of FIG. 4 that f′_(clk) whenC_(c) 54 is in parallel with L 58 has a 3.8% lower frequency (in thisexample) than when in parallel with C_(clk) 56. Again, this can be usedto reduce the size of the inductor L 58.

Still referring to FIG. 4 while taking into consideration of the MillerEffect in FIG. 5, a significant difference in the topologies is theaddition of C_(c2) to C_(d) 66 when the compensation capacitor C_(c) 54is in parallel with L 58. In this case, the decoupling resonantfrequency is:

$f_{d} = \frac{1}{2\pi\sqrt{L( {{Cd} + C_{c}} )}}$

which is a factor

$\frac{1}{\sqrt{C_{c}}}$lower than the case without C_(c) 54. Consequently, it offers theadvantage of sharing C_(c) 54 directly from C_(d) 66 for the same f_(d).

Based on the basic resonant frequency formula:

$f_{0} = \frac{1}{2\pi\sqrt{LC}}$

L 58 can be reduced by adding C_(c) 54 and considering the MillerApproximation to get C_(c1) and C_(c2). If C_(c1)+C_(clk)=α_(1x)C_(clk),where α₁ is the ratio or capacitive effect between C_(c1)+C_(clk) andC_(clk), then L 58 can be reduced as L×α₁ for the same resonantfrequency. The result is:

$L^{\prime} = {\frac{L}{\alpha_{1}} = \frac{L}{( \frac{f_{clk}}{f_{clk}^{\prime}} )^{2}}}$

α1 therefore represents the capacitive effect between C_(c1), while L′and f′_(clk) are the inductance and resonant frequency after adding theeffect of C_(c) 54. A higher α1 means a better capacitive effect and alower resonant frequency f′_(clk).

Experimental results confirm the foregoing. Smaller inductors L 58 canbe used to produce a fixed resonant frequency f₀ by incorporating acompensation capacitance C_(c) 54 in parallel with C_(clk) 56 with L 58,or with both. In addition, a fixed inductor L 58 and fixed C_(clk) 56can be used to produce a scaled frequency by incorporating C_(c) 54 inparallel with C_(clk) 56, with L 58, or with both. Significant on-chiparea can be saved by incorporating C_(c) 54. All of these results arehighly beneficial and useful when incorporating distributed LC resonantclocks.

Incorporating compensation capacitors C_(c) 54 also enables dynamicfrequency scaling. This enables a new, useful and unobvious enhancementto distributed LC resonant clocks.

Reference FIG. 6 for a distributed LC resonant clock network 100suitable for selectable frequency scaling. The distributed LC resonantclock network 100 includes a signal source 102 that operates at f₀, anamplifier 104, a first compensation capacitor C_(c) 106, a secondcompensation capacitor C_(c) 108, a capacitor C_(clk) 110, an inductor L112 and a decoupling capacitor C_(d) 114. In addition, the distributedLC resonant clock network 100 includes a first pass switch 120 and asecond pass switch 122 for selectively connecting the first and secondcompensation capacitors C_(c) 106, 108, respectively into the network100.

The distributed LC resonant clock network 100 enables multipleselectable (i.e. scalable) resonant frequencies selected by enabling ordisabling the first pass switch 120 and the second pass switch 122. Theselectable (scalable) resonant frequencies are selected in accord withthe frequencies provide above. Both compensation capacitors C_(c) 106,108 can be disabled, resulting in the resonant frequency provided abovewithout the use of compensation capacitances. If only compensationcapacitor Cc 106 is enabled by turning on pass switch 120 the result isthe resonant frequency provided above with a compensation capacitorC_(c) 106 in parallel with C_(clk) 110. Compensation capacitor C_(c) 108could be enabled by turning on pass switch 122, resulting in theresonant frequency provided above with compensation capacitor C_(c) 108in parallel with L. Both compensation capacitors C_(c) 106, 108 could beenable by turning on pass switches 120, 122, resulting in the resonantfrequency provided above with compensation capacitors C_(c) 106, 108 inparallel with both C_(clk) and L. Four different selectable resonantfrequencies can be selected by selectively turning on pass transistors120 and 122.

It is to be understood that while the figures and the above descriptionillustrates the present invention, they are exemplary only. They are notintended to be exhaustive or to limit the invention to the precise formsdisclosed, and obviously many modifications and variations are possiblein light of the above teaching. Others who are skilled in the applicablearts will recognize numerous modifications and adaptations of theillustrated embodiments that remain within the principles of the presentinvention. Therefore, the present invention is to be limited only by theappended claims.

The invention claimed is:
 1. A VLSI clock distribution network,comprising: a VLSI substrate; a clock distribution capacitor C_(clk)fabricated on said VLSI substrate, said capacitor C_(clk) having a leadconnected to ground and an open lead; a decoupling capacitor C_(d)fabricated on said VLSI substrate; a clock distribution inductor Lfabricated on said VLSI substrate, said inductor L connected to saidopen lead and to said decoupling capacitor; a buffer fabricated on saidVLSI substrate, said buffer driving said capacitor C_(clk) and saidinductor L at a clock frequency; and a compensation capacitor C_(c) inparallel with said capacitor C_(clk); wherein said clock distributionnetwork is resonant at said clock frequency, and wherein said clockfrequency is determined as:$f_{clk}^{\prime} = {\frac{1}{2\pi}{\sqrt{\frac{C_{clk} + C_{c} + C_{d}}{{L( {C_{clk} + C_{d}} )}C_{d}}}.}}$2. The VLSI clock distribution network according to claim 1, whereinsaid capacitor C_(clk) is fabricated as a MOS capacitor.
 3. The VLSIclock distribution network according to claim 1, wherein said capacitorC_(d) is fabricated as a MOS capacitor.
 4. The VLSI clock distributionnetwork according to claim 1, wherein said capacitor C_(c) is fabricatedas a MOS capacitor.
 5. The VLSI clock distribution network according toclaim 1, wherein said inductor L is a spiral wound inductor.
 6. The VLSIclock distribution network according to claim 1, wherein said inductor Lhas an inductance approximately equal to:$L = {0.0002\mspace{11mu}{l\; 〚{{\ln\frac{2l}{w + t}} + 0.5 + \frac{w + t}{3l}}〛}\mspace{11mu}{{nH}.}}$7. A VLSI clock distribution network, comprising: a VLSI substrate; aclock distribution capacitor C_(clk) fabricated on said VLSI substrate,said capacitor C_(clk) having a lead connected to ground and an openlead; a decoupling capacitor C_(d) fabricated on said VLSI substrate; aclock distribution inductor L fabricated on said VLSI substrate, saidinductor L connected to said open lead and to said decoupling capacitor;a buffer fabricated on said VLSI substrate, said buffer driving saidcapacitor C_(clk) and said inductor L at a clock frequency; and acompensation capacitor C_(c) in parallel with said inductor L; whereinsaid clock distribution network is resonant at said clock frequency, andwherein said clock frequency is determined as:$f_{clk}^{\prime} = {\frac{1}{2\pi}{\sqrt{\frac{C_{clk} + C_{d}}{L\lceil {{C_{clk}C_{d}} + {C_{c}( {C_{clk} + C_{d}} )}} \rceil}}.}}$8. The VLSI clock distribution network according to claim 7, whereinsaid capacitor C_(clk) is fabricated as a MOS capacitor.
 9. The VLSIclock distribution network according to claim 8, wherein said capacitorC_(d) is fabricated as a MOS capacitor.
 10. The VLSI clock distributionnetwork according to claim 8, wherein said capacitor C_(c) is fabricatedas a MOS capacitor.
 11. The VLSI clock distribution network according toclaim 7, wherein said inductor L is a spiral wound inductor.
 12. TheVLSI clock distribution network according to claim 7, wherein saidinductor L has an inductance approximately equal to:$L = {0.0002\mspace{11mu}{l\; 〚{{\ln\frac{2l}{w + t}} + 0.5 + \frac{w + t}{3l}}〛}\mspace{11mu}{{nH}.}}$